29 citations · 46 across the 11 of their papers we have counts for
6 papers · 1 filter
Algebraic geometry codes and some applications
Alain Couvreur, Hugues Randriambololona
This article surveys the development of the theory of algebraic geometry codes since their discovery in the late 70's. We summarize the major results on various problems such as: a…
The quadratic hull of a code and the geometric view on multiplication algorithms
Hugues Randriambololona
We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensio…
Linear independence of rank 1 matrices and the dimension of *-products of codes
Hugues Randriambololona
We show that with high probability, random rank 1 matrices over a finite field are in (linearly) general position, at least provided their shape k x l is not excessively unbalanced…
On products and powers of linear codes under componentwise multiplication
Hugues Randriambololona
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is pu…
An upper bound of Singleton type for componentwise products of linear codes
Hugues Randriambololona
We give an upper bound that relates the minimum weight of a nonzero componentwise product of codewords from some given number of linear codes, with the dimensions of these codes. I…
Asymptotically good binary linear codes with asymptotically good self-intersection spans
Hugues Randriambololona
If C is a binary linear code, let C^2 be the linear code spanned by intersections of pairs of codewords of C. We construct an asymptotically good family of binary linear codes such…